It can cause bulkingness and be harder to quilt. Depending on the size of the quilt and the size of the triangles (large quilt, small triangles) It can even add some unwanted wieght. Also sometimes they show through after quilting. At least those are the things I've been told.
In the end, it's your creation you can do as you please. There's no rules other than what works for you.
If you get an Accucut Go they'll already be cut off when you cut them.